Course the steed could be the Fred's shorter cousins...
Could be an Allosaurus which is smaller but still big. Plus it's a nice name.

T. Rex adults were a significantly larger compared with allosaurus adults. An allosaurus adult was between 8.5 and 12m in length (28-39 ft), while the average T. Rex adult was about 12-15m long (40-50 ft). The average height of an allosaurus was 17ft (a little over 5m) while T. Rex was about 23ft (7m) tall on average. The T. Rex was also substantially heavier at 14,000 lbs compared to the allosaurus at 4,000 lbs.

Yeah I plan one upgrade(Only) but a bit later.
And yes, they can get those (stat)upgrades like lizards -

Just I'm not 100% aware what where is researched and what gives. currently
Its a mess (some unlocks and gives units too. Some affects half of race - different research places. ).
It would be good if TECHS in general wud get a short description -

Oh, and @Savra make the rider different position head, also smaller and will be fine, and seeming bigger the T-rex -

For naturally blood will be of kind
Drawn-to blood, where he may it find.